The difference between mutable and "normal" is, well, mutability. I.e. you can alter the contents of NSMutableDictionary (and NSMutableArray) while you can't do that with "normal" NSDictionary and NSArray
You want to ask is "what is the difference between a mutable and a non-mutable array or dictionary." Many times there different terms are used to describe things that you already know about. In this case, you can replace the term "mutable" with "dynamic." So, a mutuable dictionary or array is one that is "dynamic" and can change at runtime, whereas a non-mutable dictionary or array is one that is "static" and defined in your code and does not change at runtime (in other words, you will not be adding, deleting or possibly sorting the elements.)
As to how it is done, you are asking us to repeat the documentation here. All you need to do is to search in sample code and the Xcode documentation to see exactly how it is done. But the mutable thing threw me too when I was first learning, so I'll give you that one!